Numerical studies of hydrate dissociation and gas production behavior in porous media during depress

Available online at www.sciencedirect.comJURNALOFScienceDirecti NATURAL GASCHEMISTRYEI SEVIERJoumal of Natural Gas Chemistry 21(2012)381-392www.elsevier.com/locate/jngcNumerical studies of hydrate dissociation and gas production behavior inporous media during depressurization processXuke Ruan'，Mingjun Yang'，Yongchen Songl*，Haifeng Liang2，Yanghui Lil1. Key Laboralory of Ocean Energy Uilization and Energy Conservation of Ministry of Education,Dalian University of Technology, Dalian 116023, Liaoning, China;2. College of Chemistry and Chemical Engineering, Taiyuan University of Technology, Taiyuan 030024, Shanxi, ChinaI Manuscript received November 18, 2011; revised January 15, 2012]AbstractIn this study, a numerical model is developed to investigate the hydrate dissociation and gas production in porous media by depressurization. Aseries of simulation runs are conducted to study the impacts of permeability characteristics, including permeability reduction exponent, absolutepermeability, hydrate accumulation habits and hydrate saturation, sand average grain size and rreducible water saturation. The effects of thedistribution of hydrate in porous media are examined by adapting conceptual models of hydrate accumulation habits into simulations to governthe evolution of permeability with hydrate decomposition, which is also compared with the conventional reservoir permeability model, i.e.Corey model. The simulations show that the hydrate dssciation rate increases with the decrease of permeability reduction exponent, hydratesaturation and the sand average grain size. Compared with the conceptual models of hydrate accumulation habits, our simulations indicate thatCorey model overpredicts the gas production and the performance of hydrate coating models is superior to that of hydrate flling models in gasproduction, which behavior does follow by the order of capillary coating>pore coating>pore filing>capillary flling. From the analysis of .t1/2, some interesting results are suggested as follows: (1) there is a“switch" value (the“switch" absolute permeability) for laboratory-scalehydrate dssciation in porous media, the absolute permeability has almost no infuence on the gas production behavior when the permeabilityexceeds the“switch”value. In this study, the “switch" value of absolute permeability can be estimated to be between 10 and 50 md. (2) Anoptimum value of initial effective water saturation Sw,e exists where hydrate dissociation rate reaches the maximum and the optimum valuelargely coincides with the value of ireducible water saturation Swr,e. For the case of Sw,e Swr.e, there are different controlmechanisms dominating the process of hydratc dissociation and gas production.Key wordsgas hydrate; numerical simulation; permeability; dissociation; gas production; depressurization1. Introductionin terms of the mechanism and the phenomena. Some meth-ods of hydrate dissociation for producing gas have been pro-Natural gas hydrates are treated as a potential energy re-posed, such as (1) depressurization [3- -5], to decrease thesource for the 21 st century because a large amount of methanepressure below the hydrate equilibrium pressure at the pre-gas is trapped in hydrate reservoirs both onshore buried undervailing temperature; (2) thermal stimulation [6,7], to raise thethe permafrost and offshore buried under the oceanic and deep .temperature above the hydration equilibrium temperature at alake sediments [1]. In the 2000s, the potential for using gasspecified pressure; and (3) inhibitor injection [8], to cause ahydrates as energy resources has stimulated national researchshift in the pressure-temperature equilibrium by injecting theand development programs in several countries such as Unitedinhibitors (such as salts and alcohols). Depressurization is a .States, Japan, China, Canada, India and South Korea [2]promising method for recovering gas from hydrate reservoirs,The gas production from hydrate reservoirs is sig-compared with the other in-situ dissociation processes of gasnificantly different from conventional oil and gas reservoirshydrate that is transformed into water and gas [9].' Coresponding auhor. Tel: +86 41-84706608 Fax: +86 411-84708015; E-mail: songyc@中国煤化工This work was supported by the National Science and Technology Major Project, China (Gra二National High TechnologyResearch and Development Program of China (863 Program, Grant No.2006AA09209-5). and MajYHc N M H Gam Program of China (973Program, Grant No.2009CB219507).CoprightO2012, Dalian Istitute of Chemical Physics, Chinese Academy of Sciences. AIl rights reserved.doi: 10.1016/S 1003-9953(1 1)60380-0382Xuke Ruan et al./ Journal of Natural Gas Chemistry Vol. 21 No,4 2012To evaluate the productivity of methane gas from theincorporated into the numerical model. The numerical resultsreservoirs by depressurization, several numerical models haveshowed the model could be competent to reproduce the per-been proposed for gas production from hydrate reservoirs inmeability characteristics and gas production behavior associ-the last two decades [3,5,9- -13]. Yousif et al. [3] treatedated with hydrate dissociation. Konno et al. [22] assumedthe hydrate dissociation by depressurization in porous mediathat hydrates occupy the capillary walls and gas/water flowsas a Kim-Bishnoi [12] dynamic process. Both gas and wa-through the center of capillaries. Through the comparisonter flows were included in their one-dimensional isothermalstudies between experimental results and numerical simula-model. Time variations of permeability and porosity duringtions by MH21 hydrate reservoir simulator, the shape of rel-the hydrate dissociation were also considered with the changeative permeability derived from Kozeny-Carman model wasof unit volume of porous medium occupied by gas and water.modified to obtain good matching for the volumes of gas andJi et al. [10] developed a 1D analytical model for gas pro-water produced during hydrate dissociation by depressuriza-duction from hydrate deposits by depressurization and theytion. Minagawa et al. [23,24] characterized water permeabil-made a series of sensitivity analyses of gas production withity of methane hydrate-bearing sediment under various con-variations of the reservoir parameters, in which the effectsditions including hydrate saturation and pore size. Ahn etfrom non-uniform porosity and permeability were also ex-al. [25], Jaiswal ct al. [26] and Johnson et al. [27] mea-amined, also Kozeny-Carman type equation was used in thesured gas-water permeability of gas hydrate-saturated poroussensitivity analysis to the permeability-porosity relationship.media synthesized in the Lab and recovered from the fieldMasuda et al. [5] developed a gas-water two-phase, finite-test well, respectively. But they did not develop an analyti-difference numerical simulator to model their hydrate disso-cal or generalized model to predict the relative permeabilityciation experimental results by depressurization. In this simu-for reservoir simulation. Kumar et al. [28] measured gaslator, Kim-Bishnoi equation was used to determine the disso-permeability of carbon dioxide hydrate-bearing porous me-ciation rate and the permeability of hydrate-bearing sandstonedia and compared the measured results with Kozeny family ofwas assumed to be the function of hydrate saturation. Moridispermeability equations given by Kleinberg et al. [29]. Theyet al. [13] developed EOSHYDR2 module for the general-inferred that for initial water saturations less than 35%, hy-purpose TOUGH2 simulator. By solving the coupled equa-drate tends to form on grain surfaces, while hydrate wouldtions of mass and heat balance, the module can model non-be a pore flling at initial water saturations greater than 35%.isothermal gas release, flow of fluid, heat transfer and phaseMeanwhile, Liang et al. [30] also conducted similar exper-behavior under any individual or combination of hydrate dis-iments for gas permeability of porous media with the pres-sociation mechanisms. Matthew et al. [14] investigated theence of methane hydrate and concluded that the change ofgas production from Class 2 and Class 3 hydrate deposits withabsolute permeability agreed with the capillary center filledthe numerical model-TOUGH-Fx/HYDRATE, their studiesmodel. Kneafsey et al. [31] carried out a series of gas per-indicated the gas production rates and efficiency depend sig-meability measurements and compared experimental data ofnificantly on the formation of porosity, the efficiency of pro-permeability to a number of models. They found that the hy-duction strategies under depressurization were compromiseddrate preferentially occupies pore bodies rather than the poreby migration of fluid from outside the system.throats in their experiments. Seol and Kneafsey [32] thenThe permeability is one of the important informationperformed a further experimental study using CT to captureneeded to reliably predict the feasibility of producing natu-methane hydrate distributions and examined the impacts ofral gas from hydrates [15,16]. Many numerical studies havepore space hydrate accumulation habits on multiphase fluiddemonstrated that permeability variation would greatly affect(gas and water) migration by comparing numerical predic-the hydrate dissociation and gas production from the poroustions with experimentally measured water saturation distribu-media with the presence of hydrates [17,18]. However, almosttions and breakthrough cures, in which the permeability wasall researchers of the above reported simulators have mademodified by incorporating three adjustable parameters baseduse of assumed values or several previously published perme-on hydrate saturation, pore size distribution and the pore spaceability correlations and models for modelling studies, and dohydrate habits. However, it should be noted that this work in-not consider the impacts of permeability characteristics, suchvolved only one experimental realization and the range of theas hydrate accumulation habits, grain size distributions, andpermeability modification factors including their implied poreso on. In recent years, several experimental efforts [19- 31]space geometries is also not clear.have focused on characterizing the permeability and relativeAll the above studies by experimental or numerical mod-permeability and some results could be available for use inelling attempt to understand how gas hydrate in the pore spacenumerical simulations, enabling simulations to better captureaffects the permeability and how it affects water and gas pro-phenomena occurring during natural gas production from hy-duction during hydrate dissociation, but some issues are stilldrate. Sakamoto et al. [19- -21] carried out a series of ex-disagreemen中国煤化工ggest the necessayperimental studies to investigate the permeability change dur-of additionalFe extents of incorpo-ing the dissociation of methane hydrate and gas production.rating the hyYHC N M H Gd pemeability char-Based on measured results, the absolute permeability and rel-acteristics into gas production simulations. One method ofative permeability were formulated as functions of methane investigation scenario is with use of numerical model in con-hydrate saturation, sand grain diameter and porosity and thensideration of the habits of hydrate present in porous media andJoumal of Natural Gas Chemitry Vol. 21 No. 42012383permeability characteristics. In this work, a 2D axisymmetricHydrate phase:numerical model has been developed for analyzing hydrate8,dissociation in porous media and predicting the gas produc-m =前(中PnSn)(3)tion behavior during depressurization process. The focus ofThe two-phase flow of gas and water can be expressed bythis work is on the effect of hydrate accumulation habits andDarey's equations:permeability characteristics on gas production. The habits ofhydrate presenting in pore space are described in this modelUi=KkrVP:(i=g.W)(4)by adopting different conceptual models of hydrate accumula-μtion habits classified in others studies [18,29], by which theyand the saturation of gas, water and hydrate accords with thedetermine the extent of the permeability reduction as a func-following relationship:tion of hydrate saturation in pore space [32]. The permeabil-Sg+Sw+Sn=1(5ity characteristics, including permeability reduction exponentN, absolute permeability, average grain size, and so on, wereThe water and gas pressures are related according to thechange as the parameters for calculations. Based on the cal-capillary force equation:culation results, the effect of permeability on the hydrate dis-sociation and gas production was discussed.P<(Sw)=Pg- Pw(6)2. Numerical model for hydrate dissociation and gas pro-2.1.2. Energy balance equationsductionThe following energy conservation equations include theGeneral governing equations for hydrate dissociation infollowing terms: conductive and convective heat transfer, heatporous media have been derived by combining the continu-inputoutput in terms of injection/production of gas and water,ity equation, mass balance equation, energy balance equation, heat of hydrate dissociation. Right hand side of equation is thekinetic reaction equation, and the equation of state for threechange in enthalpy of gas, water, hydrate and porous media.components (gas, water and hydrate). These equations arebased on the assumptions: (1) The gas hydrate in our assumed18.8，， 8T、1 θsimulation is SI type without the salt consideration; (2) Two-ror(rkeor)+ 8x(hx)-r8rphase flow accords with Darcys law, and hydrate is stagnant inporous media; (3) The absolute permeability of porous media(rPgUgrhg + TPw0wrhw) - j(PgUgxhg+is a function of hydrate saturation; (4) The generated gas does(7)not dissolve in water, and without hydrate reformation; (5)PwUwxhw)+qghg+qwhw+gh+Gin=The diffusion and the dispersion are neglected in mass trans-8portation; (6) There is no ice phase during the whole dissoci-;(1. -中)p,hr + (Snpnlh + SgPghg + SwPwhw)ation; (7) Hydrate is assumed to fill in the centre of the porespace; (8) The hydrate sediments are homogeneous and theinitial distributions of phase saturation, pressure and tempera-kc=(1-中)的+中(kmSn + kwSw + kgSg)(8)ture are uniform.gn = rmnOHp(92.1. Governing equationsThe hydrate dissociation is an endothermic and phasechange process, and the latent heat of hydrate dissociation is2.1.1. Mass balance equationsdescribed as Selim's definition [33]:rinOHp = ringHg + riw Hw + rinHn(10)The cylindrical geometry is chosen to study the gas pro-duction by depressurization. The simulation for laboratory△Hp = 446.12x 10- 132.638T(11)scale case can predict the behavior of gas production and thepressure, saturation and temperature profile. Equations (2)- -8H;_0H;(4) describe the mass balance of gas, water and hydrate.dH;= dT+ apdP: = Cp;dT +o;dP, (i= h,g,w) .Gas phase:(12)1δdH, = ordT = CprdT(13)r 8r8.(Pg'gx) + 9g + rmg=Ft(PgSg)oT(1Based中国煤化工34, the gas thotleWater phase:coefficient isYCNMH G .7 oH,(rpwDwr))x“(PwVwx)+ qw + rinw =(φρwSw)0g= ( JP)≈-1.5x 10-4(14)(2)384Xuke Ruan et al./ Joumal of Natural Gas Chemistry Vol. 21 No.4 20122.1.3. Kinetic dissociation of hydrate model2.1.5. Initial and boundary conditionsOn the basis of the model of Kim-Bishnoi, gas productiv-As shown in Figure 1, the outlet (or named as productionity of hydrate dissociation reaction is:well) is defined on the left of the core. On all the walls and themng= kuMgAs(fe- f)(15)right side of the core, no-slip boundary condition is assumed.Free convection heat transfer between the circumferential wallAs = φSnAgeo(16)and the surrounding is assumed and the boundary conditionwhere, As is the specific surface area of porous medium bear-for the ends of the core is adiabatic. Table 1 shows the initialing gas hydrate, and Ageo is the specific sharp geometry sur-conditions for the simulation.The initial conditions are based on:face area contacting non-hydrate zone. Mg is the molar massof methane gas, and ka is the dissociation constant. In ourT= To,P= Po,Sn= Sho, Sw= Swo, Sg= Sgo .simulation, the density of methane gas is calculated using(0≤r≤R,0≤x≤L)Peng-Robinson equation of state of gas. f and fe are gasfugacity and equlibrium reaction fugacity, which are usu-(23)ally replaced by local gas pressure Pg and equilibrium pres-and the following boundary conditions are imposed:sure P, respectively. Equilibrium pressure is calculated using8PEquation (17) [35].P=P(x=0), O=0(x=D), 0F=0(r=0,R),)xorPo= 1.15exp (49.3185-9459(17))ToTT=0(r= 0, R),0(x=0,L)According to the dissociation reaction of hydrate, we can(24)also obtain the following equations:Table 1.. Primary physical variable values in hydrate dssociation- rin = ringNhMw + Mg(18)from the experimental study of Masuda et al. [5]MgPrimary physical variablesvaluesriw = ring -NnMw(19)Core length L (cm)30Core pressure P (MPa)3.75Intrinsic porosity咖0.182where, Nn is hydrate number; Mg and Mw are molecularOutlet pressure Ppo (MPa)2.84weight of gas and water, respectively. - -ritn means the dis-Hydrate saturation Sno0.443sociation rate of hydrate.Gas saturation Sgo0.351Core diameter R (cm)5.02.1.4. Absolutelrelative permeability modelCore temperature To (K)275.45Intrinsic permeability Ko (md)97.98Bath temperature T (K)The absolute permeability will vary with hydrate satura-tion because the hydrate occupied the pore space interferesWater saturation Swo0.206with fluid flow. During the hydrate dissociation process, thePermeability reduction exponent N0volume occupies by gas and water continuously increases withtime as a result of gas hydrate dissociation. Masuda et al. [5]2.2. Numerical solutionexpressed firstly this relationship as fellows:K= K0(1- Sn)N(20)2.2.1. Parameters and computational grid of hydrate dissoci-where, N is called as permeability reduction exponent, and isation modela parameter depending on the pore structure. Ko is the origi-nal permeability without hydrate.The data of parameters in this simulation is obtained fromThe relative permeabilties kirw and Kkng of water and gasthe experimental study of Masuda et al., which was conductedare calculated based on modified Corey's model [36] and ex-using a Bereasandstone core sample with a cylindrical geom-pressed as follows:etry. The experiment and simulation conditions are summa-swnwrized in Table 1. The core sample is 30 cm in length andSw+Sg-Swr5.0 cm in diameter. The intrinsic porosity and intrinsic perk;rw= .1-Swt-Sgr(21)meability are 0.182 and 97.98 md, respectively. The core isinitially saturated with hydrate, water and gas (Sho = 0.443,SgngSwO = 0.206中国煤化工al pressure and tem-Sw+Sg-Sgperature arespectively. The coreing=(22)sample is plMYHCN M H Gwith Tb=275.45K.1- Swr- SgrThe pressure at the outlet located at the left of core sam-ple is maintained at 2.84 MPa for depressurization. A two-in the relative permeability model, nw=4, ng =2.dimensional numerical simulation for analyzing the hydrateJournal of Natural Gas Chemitry VoL 21 No.42012385dissociation of an axisymmetric hydrate core was performed0.00375 m and 0.15 m respectively away from the outlet alongand the corresponding gas production behaviors were ana-the central axis as shown in Figure 1, are evaluated and com-lyzed. As shown in Figure 1, the core is equally divided into 8pared. In addition, for the convenience of discussion in theblocks in radial direction and 50 blocks in axial direction, thenext sections, t1/2 is used to characterize the overall hydratemesh scale and time scale equal to 5 s can satisfy this requireddissociation rate, which is the time when 50% of the initialprecision.hydrate is dissociated [37,39,40].No slip3.1. Effect of permeability reduction exponentThe different value of permeability reduction exponent Ncould well reflect the permeability variation of a porous me-一0.00375 m, Pointi 0.15 mPoint20.3 m. Axis of symmetrydia with the presence of hydrates [41]. In this section, theeffects of permeability reduction exponent N on hydrate dis-Figure 1. Schematic of the computational grid of bhydrate dissociationsociation and gas production behavior are studied. Figure 2shows the time evolution of pressure, temperature, hydratesaturation at the Point 1 and Point 2 during hydrate dissoci-2.2.2. Solution methodation with different permeability reduction exponent N, andthe variation of t1/2 is also presented together. In Figure 3,The above mathematical equations that govern the phys-the time evolution for gas production rate and cumulative gasical process include mass transfer, heat transfer and kineticsproduction with different permeability reduction exponent Nof hydrate decomposition. The mass conservation equationsare plotted.for all the components (including water, methane gas and hy-In Figure 2, the drop decreases rapidly to the outlet pres-drate) and energy balance equation constitute a system of foursure. As hydrate dissociates, the permeability of the core sam-coupled partial differential equations which are non-linearityple increases which causes the pressure to drop faster. Theand cannot be solved analytically (exactly). Several numericalexamples have been tested to solve these equations [37,38]. Insociation reaction, the subsequent increase of the core temper-our work, fully implicit simultaneous solution method com-ature caused by the free convection heat transfer from the sur-bined with Newton's iterative method is used to solve thisrounding thermal bath can also be seen from this figure. Withmodel. The space and time derivatives of the equations arethe permeability reduction exponent N increases, the drops ofapproximated by a block- centered finite difference scheme.pressure, temperature and hydrate saturation become slowerThe central difference approximation is used for the secondand t1/2 increases gradually; both the gas generation rate andorder spatial derivatives and a backward difference is usedcumulative gas production decrease as shown in Figure 3. Afor the first order time derivatives. After nonlinear partiallarge value of N indicates that there is very lttle permeabil-differential equations are discretized into nonlinear algebraicity in the hydrate zone and there is litle mobile fluid phaseequations, Newton-Raphson iteration method is used to lin-present in the hydrate-bearing porous media, hence the pres-earize the fully implicit equations and these equations are si-sure gradient is not large and pressure drop is not transmittedmultaneously used to obtain the solutions of pressure, temper-deep into the porous media, which lead to a slow rate of hy-ature and saturation of gas, water and hydrate. The numericaldrate dissociation and a low gas productivity.results of the cumulative gas production and the temperaturefor time variations on hydrate dissociation induced by depres-3.2. Effect of absolute permeabilitysurization have been compared with the experimental results,which match well with the experimental data. The detail in-To investigate the effect of absolute permeability onformation for the validation of the model can be found in ourhydrate dissociation and gas production, simulations withother literature [38].different absolute permeability of 10 md, 50 md and 100 mdare performed. Figure 4 shows the time evolution of pressure,3. Results and discussiontemperature and hydrate saturation at the Point 1 and Point 2,and the variation of t1/2 with different absolute permeabil-An axisymmetric mathematical model for analyzing theity. The drops of pressure, temperature and hydrate saturationhydrate dissociation and gas production is developed. In thisincrease as the absolute permeability increases, and here thepaper, two points in core sample are considered, and perme-ability reduction exponent N, absolute permeability, hydratecurve of t1/2 also declines as the absolute permeability in-accumulation habit, hydrate saturation and average grain di-creases. Ina中国煤化工: curves of pressure,ameter are changed as the parameters for calculations. Basedtemperature_he case of 10 md de-on the calculation results, the simulation is used to discusscline moreIH.CN M H fferente from that forthe effect of permeability properties on the behavior of hy-the other cases of 50 md and 100 md. This phenomenon isdrate dissociation. The time variations of pressure, tempera-also reflected well in the trend of t1/2 curve. The curve oft1/2ture, hydrate saturation at the Point 1 and Point 2, which arewith low absolute permeability is steep, while the curve.386Xuke Ruan et al./ Joumnal of Natural Gas Chemistry Vol. 21 No. 420123.275.5-PI-N-5一1N 10一'1-N=15---- 12-N=534--- 12-N- 10---- 12-N=15274.5-/1-N=-5E 32: 11-.- 10 .TI-N=15---- 12-N-5274.03.0---- 72-N=I52.8L273.5 l00300400Time (min)0.4140 t一Sj1-N-15---S2-N-50.3 F。120--- S;2-N=15E 0.2斤”100.0.10.0 L2001020Permeability reduction exponent NFigure 2. Time evolution of pressure, temperature, hydrate saturation of the Point 1 and Point 2, and variation of t1/2 with different permeability reductionexponent Nbecomes more flat relatively with high absolute permeability.10000It is also similar to the results displayed in gas production be-havior. Figure 5 shows the gas generated rate and cumulativegas production over time with different absolute permeabil-88000ity, both the amount of the instantaneous gas generated andthe cumulative gas production for 10 md absolute permeabil-冒ity are smaller than that for other cases. This is because that6000low absolute permeability reduces the mobility of the fluid名and the pressure drop rate. Moreover, it can be observed thatthe whole dissociation process needs longer time because the岂4二---. .4000pressure driving force for hydrate dissociation also decreases.Meanwhile, the conclusion can be made that there may ex-ist a“switch" value for laboratory-scale hydrate dissociationin porous media. Within the“switch" value, a lower abso-22000lute permeability can lead to a lower gas generated rate andsmaller cumulative gas production, however, the effect of ab-solute perm中国煤化工on behavior is slight100and can be: permeability exceedsthe "“switch'YHC N M H Gswitch" value of ab-Figure 3. Time evolution of gas production rate and cumulative gas produc-solute permeability can be estimated to be between 10 andtion for different permeability reduction exponent N50 md.Joumal of Natural Gas Chemistry Vol. 21 No. 420123873.8一1'1.10 md一1-50 md275.0-'1-100 md3.4---- 1P2-10 md---- 1250md---- 12-100 md喜274.5: 1-10 md上3.2/1-50 md71-100 md2740----- 72-10 md3.0---- 72-50 md--- 72- 100 md2.8 L273.5 l10020000Time (min)0.16045一8.1-10 md140-二1.00 ;....2.10md0.3----2 50md120---- Si2- 100 md至800L30050150 200 250 300T ime (min) .Absolute permeability (md)Figure 4. Time evolution of pressure. temperature, hydrate saturation of the Point 1 and Point 2, and variaion of t1/2 with dfferent absolute permeabilitycommonly used conceptual models in previous literatures10 r10000[28- -32]: (1) hydrate coats the capillary walls, (2) hydrate oC-cupies capillary centers, (3) hydrate coats the grain surfaces,and (4) hydrate fills the centers of the pore space. For the con-venience in the following discussion, these models are calledI 6000as capillary coating model, capillary filling model, pore coat-一---- 10 md一---- 50 mding model and pore flling model, respectively. These con-一---- 100 md4000ceptual models of bydrate accumulation habits determine theextent of the permeability reduction as a function of hydratesaturation. Figure 6 shows the variation of gas generation rateand cumulative gas production for the four conceptual mod-els of hydrate accumulation habits and the typical Corey per-meability model. Obviously, the gas production rate and cu-mulative gas production in the case of Corey model are muchhigher than other cases. Here, the typically conventional reser-Figure 5. Time evolution of gas production rate and cumulative gas produc-voir simulation permeability model is rough and does not con-tion for different absolution permeabilitysider the effect caused by the distribution habits of hydratein porous media. The simulation result indicates this model3..3.Effect of hydrate accumulation habits and hydratecould overpredict the gas production behavior compared withsaturationthese conceptual models of hydrate accumulation habits.On the-sults also well repre-Hydrate in the porous media generally reduces perme-sent the effe中国煤化工habis on the permeability by blocking flow pathways [32], and the reduction ofability of hyHC N M H G and accordingly thepermeability depends on the locations of hydrates in porousgas production rate and the cumulative gas production. Themedia and hydrates saturation. Potential hydrate accumula-performance of hydrate coating models is superior to that oftion habits in porous media can be accounted for with fourhydrate flling models in gas production, and the gas produc-Xuke Ruan et al./ Jourmal of Natural Gas Chemistry Vol. 21 No. 42012tion behavior does follow the order of capillary coating> porecoating>pore flling>capillary flling, which is coincidentwith the change in relative permeability as listed in Table 2.. Pore coating model S-=0.3Reducing Krg from 0.063 to 0.003 results in a significant de-" Pore flling model S;=0.3terioration of gas production performance (Figure 6). That0tis mainly due to the fact that the changes in the permeabilityreduction are expected to be small when the hydrate coats thecapillary/pore walls as a thin film, while the fluid permeabilitycan be reduced more significantly if hydrate fills in the mid-dle of the capillary/pore space, plugging pore throats and the1-100 minflow channels. In other words, the coating cases correspond-ing to a better flow channel and higher gas relative permeabil-ity Krg, can obtain a better gas mobility, which in turm makes50100150200the overall mobility of fluid flow increase. Overall mobilityTime (min)well enhances the hydrate dissociation rate by increasing thefluid velocity to the outlet and improving the pressure dropwithin the hydrate region. Consequently, a coating habit of. Pore coating model s-=0.4hydrate accumulation in the porous media is favorable for the置ePore flling modelS:-0.4relative criterion of production performance (Figure 6).甚Table 2. Relative permeability for Sn = 0.443 and Sw = 0.306Conceptual models REquationsCapillary coatin 0.063Kg=(1-Sn-Sw)_2(1-Sn-Sw)尸Capillary fllig0.003 Krg=1-(Sn+Sw)2 +In(Sh+Sw)1-120 minPore coating0.032Kg=(1-Sn-Sw)n+I, n= 1.5[42]0上(1- Sn- Sw)n+2Pore flling0.010I+(Sn+Sw)0.512n=0.4(101520Computational details can be found in the literature from Kleinberget al. [29]一Pore coating modelS,-0.6I5 C. Pore fling modelS-0.6100008000Corey modelI 6000Capillary coating modelCapillary illing model色1- 180 min」4000一-- - Pore coating model-一---- Pore flling model1 20000040Figure 7. Time evolution of gas production rate for different inial hydratesaturation with the pore coating and pore flling modelFigure 6. Time evolution of gas production rate and cumultive gas produc-large pressure difference between the outlet and the inner re-tion for different permeability modelsgion. Another reason is due to the fact that the higher ini-Figure 7 shows the effect of different initial hydrate sat-tial effective permeability in the lower Sho cases leads to auration Sho with different hydrate accumulation habits on gasfaster depressurization and hydrate dissociation earlier thanproduction behavior. The initial hydrate saturations are 0.3,the higher Sno cases in the gas production process. As same0.4 and 0.6, respectively. As seen from Figure 7, a lower ini-as the reason中国煤化工eaks over time for gastial hydrate saturation leads to a higher maximum of gas gen-generated r=the case of Sho =0.3,erated rate in all cases of hydrate accumulation habits. Onethe formatiofHC.NMHGedfromboththefreeof the reasons for this is that lower Sho corresponds to highergas and the dissociated gas. As Sho increases, the decrease ofinitial gas saturation (the initial water saturation is fixed at theinitial effective permeability reduces the dissociation rate, andvalue), consequently more free gas can be driven out by thethus the gas generated from hydrate dissociation has hystere-390Xuke Ruan et al./ Journal of Natural Gas Chemistry Vol. 21 No.4 2012hydrate dissociation and gas production behavior is analyzed.sequently, the overall hydrate dissociation rate could increaseA higher permeability reduction exponent N could reflect awith the increasing initial water saturation. However, the de-lower rate of hydrate dissociation. (3) Based on the analysis ofcreasing tendency of the overall hydrate dissociation rate withthe effect of absolute permeability on hydrate dissociation andSw,e in the case of Sw,e>Swr,e as shown in Figure 9, indi-gas production behavior, there may exist a“switch" value forcates that the positive effect on dissociation rate is inappre-laboratory-scale hydrate dissociation in porous media. Withinciable, and the mobility of fluid flow dominates the overallthe“switch" value, a lower absolute permeability can lead tohydrate dissociation process, which agrees with the issue thata lower gas generated rate and smaller cumulative gas produc-the hydrate dissociation is controlled by the mass transfer fortion, however, the effect of absolute permeability on gas pro-low permeability sediments [44]. In the range of Sw,e Swr,e, has disappeared, the positive effectscompared with these conceptual models of hydrate accumula-due to the high heat capacity of water phase become sig-tion habits; the performance of hydrate coating models is su-nificant, which cause a slight increase of hydrate dissociationperior to that of hydrate flling models in gas production, andrate as the increasing initial water saturation. Based on thethe gas production behavior does follow by the order of capil-above analysis, the irreducible water saturation could be thelary coating>pore coating>pore flling>capillry flling. (5)key parameter to determine the control mechanisms of hydrateThe analysis of sensitivity to Sho with different hydrate ac-dissociation rate.cumulation habits indicates that a lower Sho leads to a highermaximum of gas generated rate but a shorter continued timefor total gas production process and the influence of the freegas and the dissociated gas on gas generated rate will shift- --..=0.25with the increase of Sho for the cases of pore coating model-.-0.35S=0.25and pore fllig model. (6) Sensitivity analysis indicates that, S.=0.35the sand grain size DA has a great effect on hydrate dissocia-置10， 100tion and gas production behavior, the dissociation rate of hy-drate and gas production increases with the decrease of DA.(7) The analysis of sensitivity to Swr.e indicates an optimum90value of initial effective water saturation Sw ,e exists where hy-80drate dissociation rate reaches the maximum and the optimumvalue largely coincides with the value of Swr,e. Meanwhile,in the case of Sw,e Swr,e, there are different.00.0.40.60.81.0control mechanisms dominating the process of hydrate disso-Initial efective water saturation S.eciation and gas production.2 with the initial effective water saturation forIn addition, a number of researches have reported theSwr = 0.25 and Swr =0.35. The solid triangle and the solid circle each rep-secondary hydrates during the depressurization process andresents the optimum initial effective water saturation for the correspondingconducted that the permeability changed dramatically when'wrhydrate re-formed and the saturation exceeded a threshold[19-22,32,45- 49]. In this work, we did not consider thisphenomenon based on the assumption of sufficient heat trans-4. Conclusionsferred from the surrounding for the laboratory-scale and timescale of this work. However, further work is needed to inves-In this study, we carry out numerical simulation for gastigate the hydrate re-formation and the permeability reductionhydrate dissociation process by depressurization on the basisin hydrate dissociation process. Additional modifications toof our 2D axisymmetric model developed. The simulation re-this numerical simulator are required and this work is cur-sults display the effect of permeability characteristics on hy-rently in progress.drate dissociation and gas production behavior. On the ba-sis of the results presented, the following conclusions can beNomenclatur中国煤化工m bearing gas hydratedrawn:As Specifi(1) t1/2 is a useful parameter to discuss the laboratory-(m2)fYHCNM HGscale hydrate dissociation process in porous media. A lowerC Specific heat (Jkg K)value of t1/2 represents a quicker hydrate dissociation proDA Average sand grain diameter (mm)cess. 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